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Rationalisation — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsRationalisation2 Marks
Question
Write the reciprocal $5+\sqrt2.$
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Answer

Given that $5+\sqrt2,$ it's reciprocal is given as $\frac{1}{5+\sqrt2}$ It can be simplified by rationalizing the denominator.
The rationalizing factor of $5+\sqrt2$ is $5-\sqrt2,$
we will multiply numerator and denominator of the given expression $\frac{1}{5+\sqrt2}$ by $5-\sqrt2,$ to get $\frac{1}{5+\sqrt2}\times\frac{5-\sqrt2}{5-\sqrt2}=\frac{5-\sqrt2}{(5)^2\big(\sqrt2\big)^2}$
$=\frac{5-\sqrt2}{25-2}$
$=\frac{5-\sqrt2}{23}$
Hence reciprocal of the given expression is $\frac{5-\sqrt2}{23}.$

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